Hey can anyone help me prove this problem? Let A and B be a subsets of R and bounded above. Let InfA=a and InfB=b. Let C= {xy ; x belongs to A, and y belongs to B} Prove that InfC=ab
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Originally Posted by salmaster Let A and B be a subsets of R and bounded above. Let InfA=a and InfB=b. Let C= {xy ; x belongs to A, and y belongs to B} Prove that InfC=ab Did you mean that to read below?
This problem isn't true as stated. 1) I think you're intending to assume that A and B are bounded below. 2) Let A = {-1, 1}, B = {-1}. Then a = -1, b = -1, so ab = 1. Also C = {-1, 1}, so inf(C) = -1. Thus inf(C) is NOT equal to ab.
Yes I'm sorry I meant bounded below.
Originally Posted by salmaster Yes I'm sorry I meant bounded below. Let then Does the statement hold in that case?
I don't think that we are supposed to prove it with specific examples of ordered pairs for A, B, and C..
Originally Posted by salmaster I don't think that we are supposed to prove it with specific examples of ordered pairs for A, B, and C.. The point is that in reply #5 so that is a counterexample to what you are trying to show. So the statement you have is false.
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